Related papers: Chance-Constrained Trajectory Planning with Multim…
This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…
Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the…
Developing safe automated vehicles that can be proactive, safe, and comfortable in mixed traffic requires improved planning methods that are risk-averse and that account for predictions of the motion of other road users. To consider these…
Prevalent solutions for Connected and Autonomous vehicle (CAV) mapping include high definition map (HD map) or real-time Simultaneous Localization and Mapping (SLAM). Both methods only rely on vehicle itself (onboard sensors or embedded…
As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as…
This paper presents fast non-sampling based methods to assess the risk of trajectories for autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods…
Learning a Gaussian mixture model (GMM) is a fundamental problem in machine learning, learning theory, and statistics. One notion of learning a GMM is proper learning: here, the goal is to find a mixture of $k$ Gaussians $\mathcal{M}$ that…
We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density…
Trajectory prediction is a crucial undertaking in understanding entity movement or human behavior from observed sequences. However, current methods often assume that the observed sequences are complete while ignoring the potential for…
Ensuring safe behavior for automated vehicles in unregulated traffic areas poses a complex challenge for the industry. It is an open problem to provide scalable and certifiable solutions to this challenge. We derive a trajectory planner…
Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…
Graphical models serve as effective tools for visualizing conditional dependencies between variables. However, as the number of variables grows, interpretation becomes increasingly difficult, and estimation uncertainty increases due to the…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…
This work investigates the design of risk-perception-aware motion-planning strategies that incorporate non-rational perception of risks associated with uncertain spatial costs. Our proposed method employs the Cumulative Prospect Theory…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
We address the challenge of enabling bipedal robots to traverse rough terrain by developing probabilistically safe planning and control strategies that ensure dynamic feasibility and centroidal robustness under terrain uncertainty.…
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework…
Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper…